Hello, I get the same result. I believe it is because one of the angles in your 
tetrahedron is acute, which would not be the case for a chemical entity.

Best wishes, Jon Cooper (Emeritus at UCL) [email protected]
Erratum and other hopefully useful things: https://crxp.org.uk

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On Thursday, 12 February 2026 at 08:14, Matthias Ullmann 
<[email protected]> wrote:

> Dear all,
>
> I have a question about the chiral volume and a potential error on this ccp4 
> website:
>
> https://www.ccp4.ac.uk/html/refmac5/theory/chiral.html
>
> On this website, it is stated:
>
> ========================
>
> Procedure to find the sign of a chiral 
> centre[¶](https://www.ccp4.ac.uk/html/refmac5/theory/chiral.html#procedure-to-find-the-sign-of-a-chiral-centre)
>
> -
>
> Put atom1 and draw bonds from the centre (atom1) to atom2, atom3, atom4 as in 
> figure 3. When the eye goes from atom2 to atom4 it should travel clockwise.
>
> -
>
> Assuming that atom2, atom3, atom4 are in the plane of the picture, then if 
> atom1 is below the plane, the chiral volume sign is plus, and otherwise it is 
> minus. If the numbering is based on the sequence rules, a positive chiral 
> volume corresponds directly to R and negative to S
>
> ========================
>
> The equation to calculate the chiral volume is usually defined as
>
> V = ⅙ (r2-r1) [(r3-r1)x(r4-r1)]
>
> If I do the calculation, I get other results. Here is an example:
>
> X1 0.0 0.0 0.0
>
> X2 0.0 1.0 1.0
>
> X3 1.0 -1.0 1.0
>
> X4 -1.0 -1.0 1.0
>
> Obviously, X1 is below the plane spanned by X2,X3, and X4, and X2->X3->X4 are 
> arranged clockwise, but the chiral volume calculated by the equation above is 
> negative (but should be positive according to the definition above).
>
> Also, L-Alanine has an S configuration, but the chiral volume around Calpha 
> (N->C(O)->Cbeta) is positive (but should be negative, see above).
>
> Do I do something wrong, or is there a mistake on the CCP4 website?
>
> I would appreciate any help/comment.
>
> Best regards
>
> Matthias
>
> --
> ========================================
> Prof. Dr. G. Matthias Ullmann
> Computational Biochemistry
> University of Bayreuth
> Universitätsstr. 30, NW I
> 95447 Bayreuth
> Germany
>
> Telephone: +49-921-55-3545
> e-mail:
> [email protected]
>
> http://www.bisb.uni-bayreuth.de/
> ========================================
>
> ---------------------------------------------------------------
>
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